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Republicans say that if President Bush maintains his strong post-convention poll numbers, he will provide coattails in key Senate races this November that eluded him in his narrow victory over Al Gore in 2000.

Those who stand to gain the most are Republicans in close, open-seat Senate races, such as Rep. Richard M. Burr in North Carolina and Pete Coors in Colorado, campaign strategists and pollsters said. Both men are trailing in their races, but both are running in states where a strong showing by Mr. Bush could trickle down.

“It’s historically unlikely that the president would win by 8 or 10 or 12 [percentage points] in some of these places and the Democratic candidate for Senate would win as well,” Republican strategist Michael McKenna said.

What has changed in the new post-convention polls, some of which show Mr. Bush with a double-digit lead, is that supporters of Democratic challenger Sen. John Kerry are now less likely to vote, Mr. McKenna said.

In 2000, Mr. Bush had no coattails, and in fact Republicans lost four Senate seats in that election. But in 2002, Mr. Bush, though not on the ballot, was instrumental in Republican candidates’ wins over Democratic incumbents in Missouri and Georgia.

This time around, a strong showing by Mr. Bush also could have the effect of putting some Republican incumbents in the safe column, including Sen. Arlen Specter in Pennsylvania and Sen. Christopher S. “Kit” Bond in Missouri.

Democrats said they don’t believe Mr. Bush will remain that high in the polls, and say Mr. Kerry is still in the mix of this race.

“You look at the polls. This is a very, very close election,” Democratic National Committee Chairman Terry McAuliffe said.

And others said they don’t believe there will be coattails this year.

“I haven’t see any evidence that in the races that will control the outcome of the U.S. Senate that George Bush has any coattails whatsoever,” said Brad Woodhouse, spokesman for the Democratic Senatorial Campaign Committee.

Mr. Woodhouse said polls show the Democratic candidates are ahead in Senate races in Oklahoma, North Carolina, Colorado and Alaska.

He specifically cited a poll in the Oklahoma race conducted for Democratic Rep. Brad Carson, who is running against Republican Tom Coburn, and shows Mr. Carson leading his opponent by two percentage points — though it also finds Mr. Bush leading Mr. Kerry by more than 30 points.

Republicans said Mr. Bush’s good standing could help the party in Senate races in Louisiana, South Carolina, Oklahoma, South Dakota and Alaska.

“Coming into this cycle, we knew that Bush at the top of the ticket would be a benefit to a majority of our candidates running in the targeted states across the country, and that remains true through this day,” said Dan Allen, spokesman for the National Republican Senatorial Committee.

Both Republicans and Democrats said Mr. Bush probably won’t have an effect on House races.

“Our expectation all along is that it’s unlikely there would be coattails on either side, and that remains the case,” said Greg Speed, spokesman for the Democratic Congressional Campaign Committee.

He pointed to polls showing that a majority of Americans believe the country is on the wrong track, and that Congress has an abysmal approval rating.

“If there’s going to be a tide, it’s going to be in our favor,” he said.

Carl Forti, spokesman for the National Republican Congressional Committee, said House Republicans didn’t see any coattails in 2000 because it was such a close race.

“We’re operating under the idea that we’re not going to have any this time either,” Mr. Forti said. “The president has opened up a slight lead now. If that is able to be maintained through Election Day, then, yes, that is going to help us.”

But it is too soon to count on that, so House Republicans aren’t, he said.